Sawtooth effect in CEPC PDR/APDR Sha Bai, Chenghui Yu, Huiping Geng, Jie Gao 2017-01-11
Motivation The bending orbit in circular collider carried out by bending magnets in arcs. Synchrotron radiation emitted when the electrons/positrons changes its trajectory. The energy loss caused the orbit distortion, and can be compensated by the next RF cavity, which is called the Sawtooth effect. CEPC strong sawtooth effect caused the magnet strength and beam real energy mismatch, the bending magnets makes the orbit distortion, quadrupoles makes the whole ring optics distortion， sextupoles makes the chromaticity correction distorted and dynamic aperture reduced significantly.
How to overcome the harm of Sawtooth effect Sawtooth effect on optics, DA, COD in PDR Sawtooth effect on optics, DA, COD in APDR Performance degradation of CEPC PDR/APDR Study Circuit Diagram How to overcome the harm of Sawtooth effect
Outline Sawtooth effect on optics and DA in CEPC PDR Sawtooth effect on optics, DA and COD in CEPC APDR Conclusions
Twiss parameters without sawtooth in PDR Lattice version: CEPC-ARC4-PDR3-IR1
Twiss parameters with sawtooth in PDR
Twiss parameters comparison of PDR NO Sawtooth Sawtooth μx 0.0800001 0.0895183 μy 0.2200000 0.2272822 βx* 0.219915 0.218720 βy* 0.001000 εx 2.15121nm 5.49688 nm εz 3.38423E-6 m 3.57412E-6 m Bunch length 2.53716622 mm 2.79435492 mm With sawtooth effect, tune change at 3 digits after the decimal point, quite little effect on tune change; β function almost no change; horizontal emittance increased nearly three times; bunch length enlarged. Since Luminosity is inversely proportional to the emittance, a large emittance growth cause the luminosity reduction.
Analysis of the horizontal emittance increase Whole ring IP to the entrance of arc Horizontal emittance εx is proportional to I5/I2 The significantly increase of εx caused by the Separators connected the PDR and the ARC.
Dynamic aperture comparison of PDR No sawtooth With sawtooth Both On-momentum and Off-momentum DA reduced a lot with sawtooth effect. Off-momentum DA beyond 1% reduced to zero. DA requirement of CEPC: on-momentum (20x,20y), off-momentum(5x,5y).
Harmonic function comparison No sawtooth With sawtooth Resonance coefficients 3000 7.505871E-11 3.246853E-02 2100 -3.365819E-10 -2.792628E-03 1020 3.166457E-09 5.405187E-02 1002 5.325543E-09 -2.019829E-02 1011 2.672939E-08 3.082794E-02 1st order chromaticity Q1’ -43.39516853 -43.42476251 Q2’ 17.82255966 17.84104701 2nd order chromaticity Q1’’ 1979.50975070 1985.65039387 Q2’’ 1098.55865448 1246.28222447 Dynamic aperture reduce due to the significantly increase of resonance coefficients with sawtooth comparing to the one without sawtooth.
Mitigation of the sawtooth effect Increase the RF cavity numbers (which is equivalent to reduce the synchrotron radiation) Optimize the IR separators design which causes the emittance growth Change the RF voltage and phase to be different between different stations Optimize the dynamic aperture, to mitigate the degradation by sawtooth effect, but it is difficult to find the sextupoles settings to satisfy both electron and positron.
Reduce Synchrotron Radiation to 1/n Horizontal orbit change With sawtooth 1/2 1/5 1/10 1/15 1/20
Twiss parameters comparison NO Sawtooth Sawtooth 1/2 1/5 1/10 1/20 μx 0.0800001 0.0895183 0.0845194 0.0817528 0.0808675 0.0804316 μy 0.2200000 0.2272822 0.2240538 0.2217279 0.2208823 0.2204458 βx* 0.219915 0.218720 0.219434 0.219747 0.219834 0.219875 βy* 0.001000 0.0009994 0.0009996 0.0009997 0.000999 εx 2.15121 nm 5.49688 nm 3.53031nm 2.48252nm 2.25480nm 2.18389nm εz 3.38423E-6 m 3.57412E-6 m 3.76753e-6m 3.87392e-6m 3.89533e-6m 3.90137e-6m Bunch length 2.53716622 mm 2.79435492 mm 2.87238027mm 2.91461168mm 2.92307962mm 2.92547315mm Synchrotron radiation reduced to 1/2 equivalent to the 100km lattice, and the RF cavity number becomes twice. In this case, the emittance reduce about 1/3. Reduce Synchrotron radiation to 1/20, horizontal emittance can almost be recovered. But the RF stations can be so many ?
Dynamic aperture No sawtooth With sawtooth 1/2 1/20 1/5 1/10 DA is far from meeting the requirements.
Summary ~mitigation of sawtooth effect by increase RF cavity numbers By reducing synchrotron radiation, the orbit sawtooth effect mitigated. Synchrotron radiation reduced to 1/2 equivalent to the 100km lattice, and the RF cavity number becomes twice. In this case, the emittance reduce about 1/3, and both on-momentum and off-momentum DA still can not be recovered. Reduce Synchrotron radiation to 1/20, horizontal emittance can almost be recovered, but DA still can not be recovered. DA is far from meeting the requirements. To compensate the DA reduction due to sawtooth effect, sextupole strength at same location is different for electron and positron.
Conclusion of PDR sawtooth effect With sawtooth effect, tune and β function almost no change. But horizontal emittance increased nearly three times. Luminosity reduced to about 1/3. The significantly increase of εx caused by the Separators connected the PDR and the ARC. Both On-momentum and Off-momentum DA reduced a lot with sawtooth effect. By reducing synchrotron radiation, the orbit sawtooth effect mitigated. Synchrotron radiation reduced to 1/2 equivalent to the 100km lattice, and the RF cavity number becomes twice. In this case, the emittance reduce about 1/3, and both on-momentum and off-momentum DA still can not be recovered. Reduce Synchrotron radiation to 1/20, horizontal emittance can almost be recovered, but DA still can not be recovered.
Outline Sawtooth effect on optics and DA in CEPC PDR Sawtooth effect on optics and DA in CEPC APDR Conclusions and Prospects
Twiss parameters without sawtooth in APDR Lattice version: CEPC-APDR-v0.0.1
Twiss parameters with sawtooth in APDR ~Horizontal unstable
Twiss parameters comparison NO Sawtooth Sawtooth μx 0.0800094 0.0000000 μy 0.2201892 0.1378555 βx* 0.250022 0.999999 βy* 0.001361 0.001459 εx 2.95372nm 3.00332nm εz 4.1139E-6 m 4.13995E-6 m Bunch length 2.93592979 mm 2.95063987 mm Since horizontal is unstable with sawtooth effect, the twiss parameters with sawtooth becomes meaningless. Optics is unstable for 50km ring.
Analysis of the horizontal emittance increase Whole ring IP to the entrance of arc Horizontal emittance εx is proportional to I5/I2 The significantly increase of εx caused by the Separators connected the PDR and the ARC.
Dynamic aperture comparison No sawtooth With sawtooth DA reduced to zero with sawtooth effect in CEPC APDR. DA is not meeting the requirement.
Reduce Synchrotron Radiation to 1/n Horizontal orbit change With sawtooth 1/2 1/5 1/2 1/10 1/15 1/20
Twiss parameters comparison NO Sawtooth Sawtooth 1/2 1/5 1/10 1/20 μx 0.0800094 0.0000000 0.0392321 0.0650136 0.0726207 0.0763370 μy 0.2201892 0.1378555 0.1758617 0.2016766 0.2108015 0.2154624 βx* 0.250022 0.999999 0.150019 0.219629 0.235873 0.243181 βy* 0.001361 0.001459 0.001391 0.001369 0.001365 0.001363 εx 2.95372nm 3.00332nm 3.40487nm 2.98311nm 2.96047nm 2.99618nm εz 4.1139E-6 m 4.13995E-6 m 4.1242e-6m 4.1174e-6m 4.1156e-6m 4.1148e-6m Bunch length 2.9359 mm 2.9506 mm 2.9422mm 2.9382mm 2.9370mm 2.9365mm By reducing the SR to 1/20, beta function still can not be recovered.
Dynamic aperture DA is far from requirement. With sawtooth No sawtooth 1/2 1/5 1/10 1/20 DA is far from requirement.
CEPC APDR orbit correction There are 16% partial double ring for APDR, so that 16% components for electron and positron have different field errors and misalignment errors. The horizontal and vertical orbit are different for electron and positron. The close orbit correction in 84% common region are conflict for electron and positron. The parameters for electron and positron at IP are not the same due to 16% PDR, the collision tuning in future could be very difficult: coupling, angular deflection, high order chromaticity……how to plan in the 16% PDR?
Summary ~mitigation of sawtooth effect by increase RF cavity numbers By reducing synchrotron radiation, the orbit sawtooth effect mitigated. Synchrotron radiation reduced to 1/2 equivalent to the 100km lattice, and the RF cavity number becomes twice. In this case, the emittance seems not improved, and both on-momentum and off-momentum DA still can not be recovered. Reduce Synchrotron radiation to 1/20, both horizontal emittance and DA can almost be recovered. To compensate the DA reduction due to sawtooth effect, sextupole strength at same location is different for electron and positron.
Conclusions of APDR sawtooth effect With sawtooth effect, horizontal unstable. DA reduced to zero with sawtooth effect. By reducing synchrotron radiation, the orbit sawtooth effect mitigated. Synchrotron radiation reduced to 1/2 equivalent to the 100km lattice, and the RF cavity number becomes twice. In this case, the emittance seems not improved, and both on-momentum and off-momentum DA still can not be recovered. Reduce Synchrotron radiation to 1/20, both horizontal emittance and DA can almost be recovered. To compensate the DA reduction and orbit distortion due to sawtooth effect, sextupole strength at same location is different for electron and positron.